She was born in Nottingham, Nottinghamshire, England and began acting at an early age. By 13 she was working on such television programs as Cracker. She eventually starred in stage productions like Jane Eyre and The History of Tom Jones, a Foundling.

She made her feature film debut, in Under the Skin (1997), and by 1998, she had received a nomination for the Academy Award for Best Supporting Actress, for Woody Allen's Sweet and Lowdown. In she won the 2002 British Independent Film Award for Best Actress in Morvern Callar, while in 2004, she received a nomination for the Academy Award for Best Actress for In America. She also received critical acclaim for her performance in Minority Report.

Morton has recently announced she will play Moors Murderer, Myra Hindley in an upcoming television film Longford, for Channel 4. It depicts the relationship between the infamous child killer, and Lord Longford, the politician who spent years campaigning for her release. Morton has been criticised by the relatives of the children who were killed by Hindley and Ian Brady, but she insists, "It is my duty as a performer to raise issues...we're afraid to look at".